Ein kinetisches Modell der Ionen in koronalen Löchern mit Welle-Teilchen-Wechselwirkung und Coulomb-Stößen

Es wird ein kinetisches Modell der Ionen in der Korona der Sonne vorgestellt. Kinetische Modelle haben gegenüber den vom Rechenaufwand her einfacheren Fl?ssigkeitsmodellen den Vorteil, daß sie keine Annahmen über die Form der Geschwindigkeitsverteilung der Ionen beinhalten und so die Beschreibung weit vom thermischen Gleichgewicht entfernter Zustände ermöglichen. Durch Integration der Verteilungsfunktionen über die senkrechten Geschwindigkeitskoordinaten werden 'reduzierte Verteilungen' eingef?hrt und eine Vlasov-Gleichung f?r diese hergeleitet. Die reduzierten Verteilungen h?ngen nur noch von jeweils einer räumlichen und einer Geschwindigkeitskoordinate ab, so daß die Vlasov-Gleichung mit vertretbarem Aufwand numerisch lösbar wird. Das Modell beschreibt die resonante Wechselwirkung der Ionen mit Plasmawellen im Rahmen der quasilinearen Theorie, wobei Energieerhaltung zwischen Wellen und Teilchen garantiert wird. Die Coulomb-Stöße werden mit Hilfe des Landau-Stoßintegrals berechnet. Die zeitabhängige Vlasov-Gleichung wird ausgehend von einem Anfangszustand numerisch gelöst, bis ein stationärer Endzustand gefunden worden ist. Dabei ist die Erhaltung von Teilchenzahl und Energie gew?hrleistet. Es werden Simulationsergebnisse für das Plasma in einem koronalen Trichter vorgestellt, die eine mit Beobachtungen übereinstimmende bevorzugte Heizung der schweren Ionen und starke Abweichungen der Verteilungsfunktionen von einer Maxwellverteilung aufweisen. Die Stabilität dieser Verteilungen wird diskutiert.A kinetic model of the ions in the solar corona is presented. In contrast to fluid models, kinetic models have the advantage of making no assumptions on the shape of the velocity distribution functions (VDFs) of the ions. Thus, they enable the description of states far away from thermal equilibrium. Integration over the velocity components perpendicular to the background magnetic field yields 'reduced VDFs'. A Vlasov equation for these reduced VDFs is derived. The reduced VDFs depend only on one spatial and on one velocity coordinate, so that the Vlasov equation for them can be solved with reasonable numerical effort. The model describes the wave-particle interaction within the framework of quasilinear theory. Energy conservation between waves and particles is guaranteed. The Coulomb collisions are calculated using the Landau collision integral. Starting from an initial condition, the time-dependent Vlasov equation is solved numerically until a stationary state has been found. The model shows good conservation of particle number and energy. Simulation results for the plasma within a coronal funnel are presented. They show a preferred heating of the heavy ions and strong deviations from a Maxwellian VDF, coincident with observations. The stability properties of these reduced VDFs are discussed

Non-Equilibrium Processes in the Solar Corona, Transition Region, Flares, and Solar Wind \textit{(Invited Review)}

We review the presence and signatures of the non-equilibrium processes, both non-Maxwellian distributions and non-equilibrium ionization, in the solar transition region, corona, solar wind, and flares. Basic properties of the non-Maxwellian distributions are described together with their influence on the heat flux as well as on the rates of individual collisional processes and the resulting optically thin synthetic spectra. Constraints on the presence of high-energy electrons from observations are reviewed, including positive detection of non-Maxwellian distributions in the solar corona, transition region, flares, and wind. Occurrence of non-equilibrium ionization is reviewed as well, especially in connection to hydrodynamic and generalized collisional-radiative modelling. Predicted spectroscopic signatures of non-equilibrium ionization depending on the assumed plasma conditions are summarized. Finally, we discuss the future remote-sensing instrumentation that can be used for detection of these non-equilibrium phenomena in various spectral ranges.Comment: Solar Physics, accepte

Interpretation of Radio Wave Scintillation Observed through LOFAR Radio Telescopes

Radio waves propagating through a medium containing irregularities in the spatial distribution of the electron density develop fluctuations in their intensities and phases. In the case of radio waves emitted from astronomical objects, they propagate through electron density irregularities in the interstellar medium, the interplanetary medium, and Earth’s ionosphere. The LOFAR radio telescope, with stations across Europe, can measure intensity across the VHF radio band and thus intensity scintillation on the signals received from compact astronomical objects. Modeling intensity scintillation allows the estimate of various parameters of the propagation medium, for example, its drift velocity and its turbulent power spectrum. However, these estimates are based on the assumptions of ergodicity of the observed intensity fluctuations and, typically, of weak scattering. A case study of single-station LOFAR observations of the strong astronomical source Cassiopeia A in the VHF range is utilized to illustrate deviations from ergodicity, as well as the presence of both weak and strong scattering. Here it is demonstrated how these aspects can lead to misleading estimates of the propagation medium properties, for example, in the solar wind. This analysis provides a method to model errors in these estimates, which can be used in the characterization of both the interplanetary medium and Earth’s ionosphere. Although the discussion is limited to the case of the interplanetary medium and Earth’s ionosphere, its ideas are also applicable to the case of the interstellar medium

LOFAR Observations of Substructure Within a Traveling Ionospheric Disturbance at Mid-Latitude

The large scale morphology and finer sub-structure within a slowly propagating traveling ionospheric disturbance (TID) are studied using wide band trans-ionospheric radio observations with the LOw Frequency ARray (LOFAR; van Haarlem et al., 2013, https://doi.org/10.1051/0004-6361/201220873). The observations were made under geomagnetically quiet conditions, between 0400 and 0800 on 7 January 2019, over the UK. In combination with ionograms and Global Navigation Satellite System Total Electron Content anomaly data we estimate the TID velocity to ∼60 ms−1, in a North-westerly direction. Clearly defined substructures with oscillation periods of ∼300 s were identified within the TID, corresponding to scale sizes of 20 km. At the geometries and observing wavelengths involved, the Fresnel scale is between 3 and 4 km, hence these substructures contribute significant refractive scattering to the received LOFAR signal. The refractive scattering is strongly coherent across the LOFAR bandwidth used here (25–64 MHz). The size of these structures distinguishes them from previously identified ionospheric scintillation with LOFAR in Fallows et al. (2020), https://doi.org/10.1051/swsc/2020010, where the scale sizes of the plasma structure varied from ∼500 m to 5 km

Interferometric imaging with LOFAR remote baselines of the fine structures of a solar type-IIIb radio burst

Context. Solar radio bursts originate mainly from high energy electrons accelerated in solar eruptions like solar flares, jets, and coronal mass ejections. A sub-category of solar radio bursts with short time duration may be used as a proxy to understand wave generation and propagation within the corona.Aims. Complete case studies of the source size, position, and kinematics of short term bursts are very rare due to instrumental limitations. A comprehensive multi-frequency spectroscopic and imaging study was carried out of a clear example of a solar type IIIb-III pair.Methods. In this work, the source of the radio burst was imaged with the interferometric mode, using the remote baselines of the LOw Frequency ARray (LOFAR). A detailed analysis of the fine structures in the spectrum and of the radio source motion with imaging was conducted.Results. The study shows how the fundamental and harmonic components have a significantly different source motion. The apparent source of the fundamental emission at 26.56 MHz displaces away from the solar disk center at about four times the speed of light, while the apparent source of the harmonic emission at the same frequency shows a speed of <0.02 c. The source size of the harmonic emission observed in this case is smaller than that in previous studies, indicating the importance of the use of remote baselines.Peer reviewe

Tuning the Exo-Space Weather Radio for Stellar Coronal Mass Ejections

Coronal mass ejections (CMEs) on stars other than the Sun have proven very difficult to detect. One promising pathway lies in the detection of type II radio bursts. Their appearance and distinctive properties are associated with the development of an outward propagating CME-driven shock. However, dedicated radio searches have not been able to identify these transient features in other stars. Large Alfv\'en speeds and the magnetic suppression of CMEs in active stars have been proposed to render stellar eruptions "radio-quiet". Employing 3D magnetohydrodynamic simulations, we study here the distribution of the coronal Alfv\'en speed, focusing on two cases representative of a young Sun-like star and a mid-activity M-dwarf (Proxima Centauri). These results are compared with a standard solar simulation and used to characterize the shock-prone regions in the stellar corona and wind. Furthermore, using a flux-rope eruption model, we drive realistic CME events within our M-dwarf simulation. We consider eruptions with different energies to probe the regimes of weak and partial CME magnetic confinement. While these CMEs are able to generate shocks in the corona, those are pushed much farther out compared to their solar counterparts. This drastically reduces the resulting type II radio burst frequencies down to the ionospheric cutoff, which impedes their detection with ground-based instrumentation.Comment: 13 Pages, 6 Figures, 2 Tables. Accepted for publication in The Astrophysical Journa

Lensing from small-scale travelling ionospheric disturbances observed using LOFAR

Observations made using the LOw-Frequency ARray (LOFAR) between 10:15 and 11:48 UT on the 15th of September 2018 over a bandwidth of approximately 25-65 MHz contain discrete pseudo-periodic features of ionospheric origin. These features occur within a period of approximately 10 min and collectively last roughly an hour. They are strongly frequency dependent, broadening significantly in time towards the lower frequencies, and show an overlaid pattern of diffraction fringes. By modelling the ionosphere as a thin phase screen containing a wave-like disturbance, we are able to replicate the observations, suggesting that they are associated with small-scale travelling ionospheric disturbances (TIDs). This modelling indicates that the features observed here require a compact radio source at a low elevation and that the TID or TIDs in question have a wavelength <~30 km. Several features suggest the presence of deviations from an idealised sinusoidal wave form. These results demonstrate LOFAR-s capability to identify and characterise small-scale ionospheric structures